Bounds on the in-plane Poisson's ratios and the in-plane linear and area compressibilities for sheet crystals

It is well known that the Poisson's ratios for 3D isotropic elastic materials vary from -1 to +1/2. These results provide reference points for comparing the Poisson's ratios of anisotropic elastic materials. Sheet crystals (SCs) with remarkably anisotropic structures, in which sheet planes do not intersect, have recently attracted major fundamental and practical interest, while the bounds on the in-plane Poisson's ratios and linear and area compressibilities have not been generically established. Based on the theory of elasticity, we here predict the fundamental bounds on the inplane Poisson's ratios and linear and area compressibilities for SCs of any crystal system. These predictions are well supported by a data-driven investigation of numerically generated elastic tensors, elastic tensors from first principles calculations for both 2D and 3D SCs, and experimentally measured elastic tensors for 3D SCs. Based on these findings, the range of 2D and 3D SC materials that increase density or planar area or maintain constant density or planar area when stretched, and increase a dimension or planar area when hydrostatically compressed is established for special applications. This work provides fundamental insights and guidelines for the discovery, understanding, and applications of SCs having these properties in tensile strain and hydrostatic pressure environments.